A view of the town of Bakhmut, the site of the heaviest battles with the Russian troops, Donetsk region, Ukraine, on Monday. AP

Russian forces carried out relentless attacks on the eastern Ukrainian city of Bakhmut on Wednesday in their quest for a breakthrough in the year-long war, although one US official predicted few short-term territorial gains for Russia.

Bakhmut had a population of about 70,000 before the war but has been ruined during months of fighting as a focal point of Russian assaults and determined Ukrainian defence.

"The enemy continues to advance in the direction of Bakhmut. He does not stop storming the city of Bakhmut," the Ukrainian military said in a morning briefing.

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A Russian takeover of the small mining city would open the way to seizing the last remaining urban centres in the industrial Donetsk province.

President Volodymyr Zelenskiy, in a video address late on Tuesday, said the battle for Bakhmut was "most difficult" but its defence was essential.

A view of the town of Bakhmut, Donetsk region, Ukraine. AP

"Russia in general takes no account of people and sends them in constant waves against our positions, the intensity of the fighting is only increasing," Zelenskiy said.

Ukrainian military analyst Oleh Zhdanov said Russian forces had driven a wedge between two villages north of Bakhmut, Berkhivka and Yahidne, in their bid to surround the city.

"This breakthrough on Bakhmut's northern flank poses a clear threat to us," he said in comments posted on social media.

Although most of the Russian attacks were focused on Bakhmut and other towns and villages in Donetsk, the Ukrainian military said its forces had repelled 85 Russian attacks on different sections of the front line over the past day.

Medics render first aid to a wounded Ukrainian soldier near Bakhmut, Donetsk region, Ukraine, on Monday. AP

Reuters was not able to verify battlefield reports.

Russia's state-run RIA news agency released a video clip it said showed Russian Su-25 fighter jets roaring over Bakhmut.

"We are glad they are ours," says a man in the clip identified as a fighter of the mercenary Wagner Group, adding the jets helped them "psychologically".

Ukrainian aircraft launched three strikes on areas of concentration of Russian forces, the Ukrainian military said in a statement on Tuesday night.